The fundamental results of A. Connes which determine a complete set of isomorphism classes for most injective factors are discussed in detail. After some introductory remarks which lay the foundation for the subsequent discussion, an historical survey of some of the principal lines of the investigation in the classification of factors is presented, culminating in the Connes-Takesaki structure theory of type III factors. After a discussion of injectivity for finite factors, the main result of the paper, the uniqueness of the injective II1 factor, is deduced, and the structure of II∞ and type III injective factors is then obtained as corollaries of the main result.